cite, several different works have tried to model non-Poisson spike counts [1]}, [2]}, [3]}, [4]}. In particular, the NB response has been implemented to model spike count data in the visual pathway [5]}, which is beneficial for understanding the representation of sensory information in the brain. If we consider the case when the spike count data is over-dispersed, then modeling the neuronal response generated from the NB distribution is a natural choice, as the NB distribution assumes that the variance of the spike count data is larger than its mean value. At the same time the NB distribution can also be considered to be a generalization of the Poisson distribution where the rate parameter of the Poisson distribution is represented as a Gamma distribution. Thus, the Gamma-Poisson mixture, models the spike count of the \(j\) -th trial at time \(i\) , denoted as \(y_{ij}\) , as a Poisson distribution. Consequently, the mean value, \(\lambda _{i}\) , of the count data from time bin \(i\) , becomes a Gamma distribution. These processes are given as
\(y_{ij}\mid \lambda _{i} \sim \mathrm {Pois}(\lambda _{i}) =& \frac{\lambda _{i}^{y_{ij}}}{y_{ij}!}e^{-\lambda _{i}}, \\\lambda _{i}\mid r,\theta _{i} \sim \mathrm {Ga}\left(r,\frac{\theta _{i}}{1-\theta _{i}}\right) =& \lambda _{i}^{r-1}\frac{\exp \left(-\lambda _{i}\frac{\theta _{i}}{1-\theta _{i}}\right)}{\left(\frac{1-\theta _{i}}{\theta _{i}}\right)^{r}\Gamma (r)}. \) 
